Question
Download Solution PDFA 275 m long train overtakes a man moving at a speed of 6 km/h (in same direction) in 45 seconds. How much time (in seconds) will it take this train to completely cross another 280 m long train, moving in the opposite direction at a speed of 26 km/h?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
A 275 m long train overtakes a man moving at a speed of 6 km/h (in the same direction) in 45 seconds.
Another train length = 280 m, moving in the opposite direction at a speed of 26 km/h.
Formula used:
Relative speed (same direction) = Speed of train - Speed of man
Relative speed (opposite direction) = Speed of train + Speed of other train
Distance = Speed × Time
Calculation:
Speed of man = 6 km/h = 6 × (5/18) m/s = 5/3 m/s
Relative speed (same direction) = Speed of train - Speed of man
⇒ (Speed of train - 5/3) m/s = Distance / Time
⇒ (Speed of train - 5/3) = 275 / 45
⇒ Speed of train = (275 / 45) + 5/3
⇒ Speed of train = 350 / 45 m/s = 7.78 m/s
Relative speed (opposite direction) = Speed of train + Speed of other train
Speed of other train = 26 km/h = 26 × (5/18) m/s = 7.22 m/s
⇒ Relative speed = 7.78 + 7.22 = 15 m/s
Combined length of both trains = 275 m + 280 m = 555 m
Time = Distance / Speed
⇒ Time = 555 / 15 = 37 seconds
∴ The correct answer is option (2).
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